Color superfluidity and Baryon formation in ultracold fermions

We study fermionic atoms of three different internal quantum states (colors) in an optical lattice, which are interacting through attractive on site interactions, U < 0. Using a variational calculation for equal color densities and small couplings, vertical bar U vertical bar vertical bar U-C vertical bar, triplets of atoms with different colors form singlet fermions (trions). These phases are the analogies of the color superconducting and baryonic phases in QCD. In ultracold fermions, this transition is found to be of second order. Our results demonstrate that quantum simulations with ultracold gases may shed light on outstanding problems in quantum field theory.